Abstract: We present an algorithm, based on approximation by Laguerre polynomials, for computing a point on the stable manifold of a stationary solution of an autonomous system. A superconvergence phenomenon means that the accuracy of our results is much higher than the usual spectral accuracy. Both the theory and the implementation of the method are considered. Finally, as an application of the algorithm, we describe a fully spectral approximation of homo- and heteroclinic orbits.

24.Michael
Shub, Global stability of dynamical systems, Springer-Verlag,
New York, 1987. With the collaboration of Albert Fathi and Rémi
Langevin; Translated from the French by Joseph Christy. MR 869255
(87m:58086)